Trends in bulk compressibility of Mo2−xWxBC solid solutions

The Mo2−xWxBC system is of interest as a material with high hardness while maintaining moderate ductility. In this work, synchrotron diffraction experiments are performed on Mo2−xWxBC solid solutions, where x = 0, 0.5, and 0.75, upon hydrostatic compression to ∼54 GPa, ∼55 GPa, and ∼60 GPa, respectively. Trends in bulk modulus, K0, are evaluated by fitting collected pressure-volume data with a third-order BirchMurnaghan equation of state, finding K0 = 333(9) GPa for Mo2BC, K0 = 335(11) GPa for Mo1.5W0.5BC, and K0 = 343(8) GPa for Mo1.25W0.75BC. While K0 demonstrates a slight increase when Mo is substituted by W, calculated zero pressure unit cell volume, V0, exhibits the opposite trend. The decrease in V0 corresponds to an increase in valence electron density, hardness, and K0. Observations corroborate previously reported computational results and will inform future efforts to design sustainable materials with exceptional mechanical properties.


Introduction
The automotive, aerospace, defense, and health care industries, among others, depend on materials with enhanced hardness. 1 Efforts to discover superhard materials, with a Vickers hardness (H V ) ≥ 40GPa, have largely relied upon simple design rules and trial-and-error approaches. 2 Accordingly, attempts to mimic the structural and mechanical properties of diamond (H V ≈ 90 − 100GPa), the prototypical superhard material, have manipulated light, main group elements to achieve the desired strong, dense 3D network of short covalent bonds. [3][4][5][6] Cubic boron nitride (c-BN, H V = 55 GPa) and BC 2 N (H V = 65 GPa) are examples of this type. [7][8][9] However, the synthesis of diamond and other hard materials in its class is often cost-prohibitive, requiring extreme temperatures and pressures. 2 To combat the exorbitant synthetic costs, researchers have directed focus towards another class of hard materials: transition metal (TM ) borides such as ReB 2 (H V = 45 GPa) and WB 4 (H V = 43 GPa). 10,11 Integration of the TM s simplifies material synthesis because conventional arc melting processes can yield the desired structures. In these structures, the light boron atoms support the formation of covalent bonding networks, while the heavy TM s are intrinsically incompressible due to their high valence electron density, properties well understood to promote hardness. 1,3,12 Incorporating TM s into superhard materials discovery efforts unearths a vast, underexplored compositional space and provides an excellent opportunity to investigate new materials compositions with optimized mechanical properties. Although superhard materials of this type are often impractical as candidates for industrial use as the TM s employed can be expensive and scarce, sustainability concerns can be addressed through elemental substitution of the expensive, rare-earth TM s with more earth-abundant metals. 2 TM substitution can also modify valence electron concentration (VEC ) and atomic size effects to tailor mechanical properties. For instance, substitution of W with Ti, Zr, Hf, Mo, Ta, Mn, or Cr improves hardness of WB 4 -based solid solutions from H V = 43 GPa to greater than H V = 50 GPa. [13][14][15] Similarly, Mo 0.9 W 1.1 BC demonstrates improved hardness compared to its isostructural parent composition, Mo 2 BC, with H V = 26.5 GPa and H V = 42.1 GPa, respectively, at 0.49 N indentation load. 16 The Mo 2−x W x BC solid solution system is of particular interest because it provides the unique opportunity to optimize hardness while maintaining moderate ductility, contradictory extrinsic properties often challenging to predict and control. Although hardness and ductility are difficult to predict directly, bulk modulus (K) and shear modulus (G) are intrinsic material properties that correlate to ductility, brittility, and hardness, allowing for indirect estimations. Pugh's ratio, G/K, estimates ductility in inorganic compounds, as compounds with G/K < 0.57 are considered ductile and those ≥ 0.57 brittle. 17 The elastic moduli of hard, isostructural MoWBC and Mo 2 BC have been investigated using density functional perturbation theory, finding G/K = 0.579 and 0.576, respectively. 16 Thus, it is suggested that ductility is preserved in the Mo 2−x W x BC system regardless of the TM ratio, even though elemental substitution of Mo with W results in increased hardness. A separate ab initio study of Mo 2 BC also suggests moderate ductility due to the presence of both the metallic interlayer bonding and stiff carbide and boride layers. 18 The ability to maintain ductility in high-hardness materials is an intriguing concept as conventional superhard materials are typically brittle (i.e. diamond G/K = 1.21). 19 Experimental determination of trends in K within Mo 2−x W x BC solid solutions is a pragmatic step towards informing computational efforts and developing an improved understanding of the balance between elastic moduli, hardness, and ductility in TM -based hard, incom-

Experimental Methods
Three isostructural Mo 2−x W x BC compositions, where x = 0, 0.5, and 0.75, were synthesized in a previous work. 16 Stoichiometric ratios of the starting materials, including Mo (Alfa Aesar, 99.95%), W (Alfa Aesar, 99.5%), crystalline B (Alfa Aesar, 99.5%), and graphite (Sigma-Aldrich, 99.99%), were weighed out to a total mass of 0.25 g and pressed into 6 mm pellets. The pellets were arc melted in a flowing argon atmosphere on a water-cooled copper hearth, flipping each sample at least twice to ensure homogeneous melting and thorough mixing of the elements.
To evaluate bulk compressibility, synchrotron diffraction experiments were performed on each Mo 2−x W x BC composition under compression. A Diamonite T M mortar and pestle was used to grind the arc melted samples to a fine powder, mixing in 5% ruby powder and 10% platinum powder as pressure calibrants. 21 The finest particles were isolated from the bulk powder through solvent suspension in methanol. This process was repeated on the isolated material to achieve an even finer particle size. Sample/Pt mixtures were loaded into a 45-60 µm diameter sample chamber which was laser milled into stainless steel gasket material after pre-indention to a thickness of ∼40 µm from an initial thickness of 250 µm. To achieve near-hydrostatic conditions, sample mixtures were gas loaded into the sample chamber with a neon pressure medium. High pressure conditions were achieved using a symmetric DAC with 200 µm diameter flat culet diamond anvils.
Facilities of the High Pressure Collaborative Access Team (HPCAT) at beamline sector 16-ID-B of the Advanced Photon Source (APS) were used to perform the synchrotron experiments. The Mo 2−x W x BC samples were incrementally compressed to ∼55-60 GPa in steps of 1-5 GPa at ambient temperature. At each step, monochromatic X-rays (λ = 0.4066 Å) and a Pilatus detector were used to collect angle-dispersive diffraction spectra in axial geometry.
X-ray energy was ∼30.5 keV and the beam was focused to 5 µm × 4 µm. A cerium dioxide standard was used to calibrate sample-to-detector distance (209.7 mm), detector tilt, and detector rotation. Collected 2D diffraction images were converted from polar coordinates to Cartesian coordinates using FIT2D. 22 Lattice parameters were determined from the diffraction data using the Le Bail method as implemented in the MAUD (Materials Analysis Using Diffraction) software package. 23 Because near-hydrostatic conditions were maintained, lattice strain was not refined. An isothermal, third-order Birch-Murnaghan EOS (Equation 1) was fit to the relative cell volume versus pressure curves using EOSFit software to determine K 0 and the first pressure derivative of the bulk modulus, K 0 . 24

Results and Discussion
To determine K 0 of three Mo 2−x W x BC solid solutions (x= 0, 0.5, 0.75), synchrotron diffraction patterns were collected upon hydrostatic DAC compression. The diffraction data were evaluated using MAUD software, refining lattice parameters of both the borocarbides and internal platinum pressure calibrant to monitor pressure. 21 Figure 1 illustrates the diffraction data as an intensity map for each Mo 2−x W x BC solid solution, demonstrating compression of the crystal structure as peaks shift to higher Q-space values with increasing pressure. In all of the   (7) collected spectra, observed peaks could be indexed to either the orthorhombic borocarbide phase or to the platinum or ruby internal pressure calibrants, with no indication of phase transformations across the entire pressure range.
The refined relative volume (V 0 /V ) is plotted as a function of calculated pressure for each solid solution in Figure 2, while a third-order Birch-Murnaghan EOS (Equation 1) is fit to each dataset to determine V 0 , K 0 , and K 0 . 24 Table 4 presents the experimentally determined   (7) To evaluate correlations among composition and the observed trends in bulk moduli and other mechanical properties, it is important to first consider the Mo 2−x W x BC (0 ≤ x < 1.1) crystal structure. The unit cell is highly anisotropic, crystallizing in an orthorhombic space group (Cmcm) isostructural to the Mo 2 BC parent phase, and visualized in Figure 4 using VESTA software. 25     For the experimentally evaluated Mo 2−x W x BC solid solutions, K 0 appears to directly correlate with increasing W content and decreasing Mo content, from K 0 = 333(9) GPa  for Mo 2 BC to K 0 = 373(4) GPa for Mo 0.9 W 1.1 BC. These findings indicate that bulk compressibility of the Mo 2−x W x BC structures, particularly the tungsten-rich compositions, are comparable to values reported for WB 4 (K 0 = 369(9) GPa and K 0 = 1.2(5)). 26 Additionally, calculated V 0 of Mo 2−x W x BC generally decreases as W content increases, in agreement with X-ray diffraction results reported previously, and can be explained by shorter, stronger bonding among the TM s. 16 Reduced crystal volume also correlates to increased valence electron  In addition to the exceptional bulk moduli, hardness, and ductility of this system, understanding these properties in the context of the anisotropic lattice strain and texture development when exposed to nonhydrostatic stresses can inform future efforts to implement Mo 2−x W x BC solid solutions in applications requiring wear-resistance. Previously, nonhydrostatic compression experiments on Mo 0.9 W 1.1 BC investigated anisotropic deformation behavior and found that the (002) and (200) planes parallel to the long b-axis support the greatest differential strain. 27 These planes are orthogonal to the covalently bonded boron chains, which likely provide additional elastic support and decrease the susceptibility to slip.

Conclusions
The Mo 2−x W x BC system demonstrates the potential to optimize hardness, ductility, and sustainability in synthetically accessible inorganic materials for applications requiring wearresistant, superhard materials. In this work, bulk compressibility of Mo 2−x W x BC solid solu-tions, where x= 0, 0.5, and 0.75, were evaluated through in situ hydrostatic, high-pressure synchrotron diffraction experiments to ∼54 GPa, ∼55 GPa, and ∼60 GPa, respectively.
The calculated Birch-Murnaghan EOS for each composition demonstrate an increase in K 0 with rising W content and are in good agreement with previous computational studies. Furthermore, V 0 decreases as Mo is substituted by W, corresponding to the increase in valence electron density, hardness, and K 0 . Experimental determination of trends in K 0 within Mo 2−x W x BC solid solutions can inform future computational and experimental design endeavors in the search for environmentally sustainable materials with superb mechanical response.